In order to connect together two sets of initially-independent fibers by using one of the methods applied to ribbons of optical fibers, a known method consists in creating a ribbon from each of the two sets of fibers prior to connection. The sheathed fibers in each set are assembled together side-by-side by means of a common resin coating that constitutes the outer coating of the resulting ribbon. Assembling fibers together in ribbons is time-consuming and costly, and it requires bulky equipment. Such assembly physically secures the fibers together.